Factor the expression 63zm^2-84zmn28zn^2 | SnapXam

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 Exercise

$63zm^2-84zmn+28zn^2$

 Step-by-step Solution

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1

Factor the polynomial $63zm^2-84zmn+28zn^2$ by it's greatest common factor (GCF): $7z$

$7z\left(9m^2-12mn+4n^2\right)$

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2

The trinomial $\left(9m^2-12mn+4n^2\right)$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=-12^2-4\left(9\right)\left(4\right) = 0$

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3

Using the perfect square trinomial formula

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{9m^2}\:and\:b=\sqrt{4n^2}$

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4

Factoring the perfect square trinomial

$7z\left(3m-2n\right)^{2}$

Final answer to the exercise  

$7z\left(3m-2n\right)^{2}$

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Integrate by partial fractions
Product of Binomials with Common Term
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 Main Topic: Perfect Square Trinomial

Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is twice the product of the square roots of the first and third terms. The sign of the middle term will tell us whether the factorization will involve a binomial that is either a sum or a difference (signs need to match)

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